Transport properties: conductance and thermopower Rok Žitko Institute Jožef Stefan Ljubljana, Slovenia

Transport in nanostructures

Landauer formalism

Density of states per unit length: (Includes factor 2 for spin)

For T(E)=1 (ballistic conductor): In general, at T=0: Multi-channel leads: resistance quantized contact resistance

Scattering theory quasiparticle phase shifts Spin symmetry, single effective channel:

Keldysh approach One impurity: Relection symmetric problems: Also known as the Meir-Wingreen formula

Conductance of quantum dot (SIAM)

Finite temperatures

Effect of the magnetic field

A B A B I V~0 V dI/dV V>0 V

A B A B ħ w I V~0 eV>h w Inelastic scattering dI/dV ħ w ħ w V V Information about internal degrees of freedom !

Linear response theory for calculating the conductance of nanostructures Kubo (1957)

Standard approach: Difficulty: the slope is difficult to calculate reliably!

Solution: we can work with the global operator N n itself!

Test case: single-impurity Anderson model

Proposed application: conductance of a S-QD-N structure • Open problem: the transition from G=4e 2 /h to G=2e 2 /h conductance as the gap closes 1) 2) 4) 3) Anyone interested?

Transport integrals, thermopower

B=0 (charge) Seebeck coefficient d =0 (particle-hole symmetric point) spin Seebeck coefficient

Žitko, Mravlje, Ramšak, Rejec, manuscript in preparation.

Spin thermopower is a sensitive probe of the response of the system in magnetic field.